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Пишет Bananeen ([info]bananeen)
@ 2020-03-07 19:11:00

Previous Entry  Add to memories!  Tell a Friend!  Next Entry
Идея украдена у euch. Я попытаюсь как-то упорядочить накопившиеся ссылки на разную литературу.

Algebraic geometry.
1. Why study algebraic geometry?
2. Best Algebraic Geometry text book? (other than Hartshorne)
3. Ravi Vakil, Foundations of Algebraic Geometry
4. The Stacks Project
5. Gortz, Wedhorn - Algebraic Geometry I
6. Derived Algebraic Geometry Reading List
7. Motives, Tannakian categories & Intersection Theory Reading List
8. Voevodsky et al, Motivic Homotopy Theory
9. Classical papers in algebraic geometry
10. References for etale cohomology
11. References for Mori theory
12. K-theory and Intersection theory - Gillet
*. Algebraic geometry, as seen by Andrei Tyurin

Deformation theory.
1. Talpo, Vistolli - Deformation theory from the POV of fibered categories
2. Manetti - Deformation theory via DGLA
3. Manetti - DGLA and formatl deformation theory


Basics of manifolds and differential geometry.
1. Introductory texts on manifolds
2. Brian Conrad, Differential Geometry handouts
3. Torstern Wedhorn, Manifolds, Sheaves and Cohomology, To be published in 2016
4. Yaiza Canzani, Analysis on manifolds via the Laplacian
5. A Spinorial Approach to Riemannian and Conformal Geometry
6. Course on Spin Geometry
6*. Other materials from Edinburgh Mathematical Physics Group
7. Vera Serganova, Lie groups
8. Jeff Viaclovsky, courses in differential geometry
9.Berkeley's Lie Groups Lecture notes
10. Notes on global analysis
11. Differential Topology - Zurich


Complex geometry
1. Learning complex geometry
1*. References for complex analytic geometry?
2. Jean-Pierre Demailly, Complex Analytic and Differential Geometry
3. Eberhard Freitag Lecture notes on Complex Spaces, Kahler manifolds, Hodge theory
4. Marco Manetti, Lectures on deformations of complex manifolds
5. Eleny Ionel, Complex Differential Geometry
6. Blocki, Several Complex Variables
7. Gábor Székelyhidi, Introduction to Extremal Metrics
8. Freitag - Kaehler manifolds - очень ясное изложение (p,q) разложения на комплексном многообразии

Symplectic/contact geometry/topology
1. Contact geometry links

Representation theory
1. Dennis Gaitsgory, Geometric Representation Theory

Topology
1. Neil Strickland, A bestiary of topological objects
2. Allen Hatcher, Algebraic Topology, Vector Bundles and K-theory, Spectral Sequences, Topology of numbers
3. Peter May, A Concise Course in Algebraic Topology
3*. Peter May, More Concise Algebraic Topology
4. Ioannis Zois, 18 Lectures on K-theory
4*. K-theory texbook recommendations, MathOverflow
5. Notes on the Atiyah-Singer Thm, Liviu Nicolaescu
6. L.Cohen - Topology of Fiber Bundles
7. Schwede, Symmetric Spectra
8. Davis & Kirk
9. Rudyak, Thom spectra, cobordism
10. Bordism:
D. Freed, Bordism: Old and New
H. Miller, Notes on Cobordism
T. Weston, An introduction to Cobordism theory
11. S. Kochman, Bordism, Stable Homotopy and Adams Spectral Sequences
12. Topological K-theory notes
13. Martelli - An introduction to geometric topology


Homological algebra.
1. Beilinson's lectures on categories

Mathematics around Physics
1. Kapustin, literature on Advanced Mathematical Methods of Physics
2. Peter Woit, Quantum Theory, Groups and Representations: An Introduction
2*.Peter Woit
3. Mirror Symmetry
4. Sheldon Katz
5. Denis Auroux, Topics in Mirror Symmetry
5.*Denis Auroux
6. IAS, Quantum Field Theory
7. NLab, Geometry of physics
7*. Urs Schreiber
8. Urs Schreiber, Differential cohomology in a cohesive topos
9. Frederic Paugam, Towards the mathematics of quantum field theory
10. Nick Sheridan, Mirror Symmetry stuff
11. Ko Honda, Conformal Field theory



Unsorted
1. Eckhard Meinrenken, Clifford Algebras and Lie Theory, recomended here
2. Marco Gualtieri, Dirac Geometry
3. Books of Dominic Joyce
4. Stiven Sivek, Contact geometry in 3 dimensions
5. Akhil Mathew's Notes from Harvard Courses
6. Jason Bland's Notes from Harvard Courses
7. Dan Freed, K-theory
7*. Dan Freed, Bordism: Old and New
7**. Classical Field Theory and Supersymmetry, Dan Freed
7***. Geometry of Dirac Operators, Dan Freed
7****. Dan Freed
8. Vaughan F.R. Jones, Von Neumann Algebras
9. Stephan Stolz, lecture notes
10. Tim Perutz, Topics in Floer theory
11. Sheel Ganatra, Aspects of Fukaya categories
12. Victor Ginzburg, Lectures on Noncommutative Geometry
13. Intro into dynamical systems, Milnor
14. Hodge theory various articles
15. Vistolli - NOTES ON CLIFFORD ALGEBRAS,
SPIN GROUPS AND TRIALITY






Other lists:
1. Akhil Mathew
2. Maxim Stykow
3. Charles Siegel
4. Hero Lee Tanaka
5. Andrew Nietzke
6. Nilay Kumar - Complex geometry, derived algebraic geometry
7. Sustretov


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